Export .obj file with png texture
The .mtl file is only a material definition file which contains references to textures.

if you want to export obj with .mtl and textures you need to make sure you follow these steps:

In your OBJ export menu:


Make sure material export is ticked





Set the path mode on COPY




You will see that in your target folder you now have


An obj file which contains your mesh information
An mtl file which contains material definition
All tetxure files referenced in the .mtl